Question

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.

−b b2 − 4ac 2a

Use the part of the quadratic formula that you chose above and find its value, given the following quadratic equation:

4x2 + 6x + 2 = 0

Numerical Answers Expected!

Answer 1

Hello,

if b²-4ac>0 then the equation has 2 reals roots
if b²-4ac=0 then the equation has one real root with multiplicity 2
if b²-4ac<0 then no real root.

4x²+6x+2=0

Δ=6²-4*4*2=36-32=4=2² ==> 2 reals roots

==>x=(-6-2)/8=-1 or x=(-6+2)/8=-1/2

One other way is:

4x²+6x+2=0
==>2(2x²+3x+1)=0
==>2x²+3x+1=0
==>2x²+2x+x+1=0
==>2x(x+1)+1(x+1)=0
==>(x+1)(2x+1)=0
==>x=-1 or x=-1/2

Answer B